Update (10:15 a.m.)
Independence National Historical Park–aka the Liberty Bell and friends–will re-open gradually today, according to park ranger Adam Duncan, who handles public affairs.
After the NPS conducts a safety check, a facilities check, and corrals park service workers into work today, the tourist attractions on Independence Mall will be ready for business. Right now, the Independence Visitor Center is back open, and previously blocked-off areas have been un-blocked-off. Bonus: When Independence Hall opens, it'll be free to the public today, on a first-come, first-served basis.
Call the Independence Visitor Center and you'll get an automated response telling you that it's closed because of the government shutdown. Visit the National Parks Service website, and you'll get this insta-message.
The government may be open (until January, that is), but the most visible aspect of Philadelphia's tourism industry does not appear to be. The Department of the Interior (which runs the NPS, and appears to be at least partially open for business) said they'd get back to me with details about the status of Independence National Historical Park, and I'll update the post when they do.